How do you divide #(x^2+5x+1)div(x+3)# using synthetic division?

1 Answer
Jan 20, 2018

Answer:

#color(magenta)((x^2+5x+1) / (x+3) = x+2# and remainder of# color(magenta)(-5/(x+3)#

Explanation:

#color(white)(aaaa)##-3##color(white)(aaaa)##|##color(white)(aaaa)##1##color(white)(aaaa)##5##color(white)(aaaaa)##1##color(white)(aaaaaa)##color(white)(aaaaaa)#

#color(white)(aaaaaa)##color(white)(aaaaa)##|##color(white)(aaa)##color(white)(aaaa)##-3##color(white)(aaaa)##-6##color(white)(aaaaa)##color(white)(aaaaaa)#

#color(white)(aaaaaaaaaa)#---------------------------------------------

#color(white)(aaaa)##color(white)(aaaaaa)##color(white)(aaaaaa)##1##color(white)(aaaaa)##2##color(white)(aaaaa)##color(white)(a)##-5##color(white)(aaaaaa)###

The remainder is #color(magenta)(=-5/(x+3)#

The quotient is #color(magenta)(=x+2#